MGSC 1205 Quantitative Methods I

Size: px
Start display at page:

Download "MGSC 1205 Quantitative Methods I"

Transcription

1 MGSC 1205 Quantitative Methods I Class Seven Sensitivity Analysis Ammar Sarhan 1

2 How can we handle changes? We have solved LP problems under deterministic assumptions. find an optimum solution given certain constant parameters (costs, price, time, etc) How well do we know these parameters? Usually not very accurately rough estimates Conditions in most world situations are dynamic & changing prices of raw materials change product supply changes new machinery is bought to replace old employee turnover occurs 2

3 Sensitivity Analysis Post-optimality analysis: examining changes after the optimal solution has been reached. input data are varied to assess optimal solution sensitivity. Basic Question: How does our solution change as the input parameters change? How much does the objective function change? How much do the optimal values of the decision variables change? Do our results remain valid (If the parameters change...)? 3

4 Example: High Note Sound Company The company Manufactures quality CD players and stereo receivers. Each CD player sold results in $50 profit, while each receiver yields $120 profit. Each product requires skilled craftsmanship. Each CD player requires: 2 hours electrician s time and 3 hours technician s time Each receiver requires: 4 hours electrician s time and 1 hour technician s time Hours available: 80 for electrician s time, 60 for technician s time Objective: maximize profit 4

5 B5:C5 D6 D8:D9 5

6 Answer Analysis Target Cell (Max) Cell Name Original Value Final Value $D$6 Profit $0.00 $2, Cell Name Original Value Final Value $B$5 Solution value CD players $C$5 Solution value Stereo receivers This column indicates whether a constraint is exactly satisfied (LHS=RHS) Cell Name Cell Value Formula Status Slack $D$8 Electricians' Time $D$8<=$F$8 Binding 0.00 $D$9 Audio Technicians' Time $D$9<=$F$9 Not Binding

7 Answer Report Target Cell (Max) Cell Name Original Value Final Value $D$6 Profit $0.00 $2, Cell Name Original Value Final ValueThis column indicates $B$5 Solution value CD players the amount of unused $C$5 Solution value Stereo receivers resource Cell Name Cell Value Formula Status Slack $D$8 Electricians' Time $D$8<=$F$8 Binding 0.00 $D$9 Audio Technicians' Time $D$9<=$F$9 Not Binding

8 Sensitivity Report Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$5 Solution value CD players E+30 $C$5 Solution value Stereo receivers E Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $D$8 Electricians' Time $D$9 Audio Technicians' Time E This table presents information regarding the impact of changes to the OFCs (i.e., the unit profits of $50 & $120) Allowable Increases & Allowable Decreases: they are the range of values for which we can change the OFCs, and still have current Corner Point remain as Optimal Solution This is the whole point of doing the analysis! 8

9 Sensitivity Report Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$5 Solution value CD players E+30 $C$5 Solution value Stereo receivers E Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $D$8 Electricians' Time $D$9 Audio Technicians' Time E Allowable Increases & Allowable Decreases: they are the range of values for which we can change the OFCs, and still have current Corner Point remain as Optimal Solution 9

10 Sensitivity Report Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$5 Solution value CD players E+30 $C$5 Solution value Stereo receivers E Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $D$8 Electricians' Time $D$9 Audio Technicians' Time E This table presents information on impact of changes in RHS. Final Value: the values of how much of each resource (constraint) is used up in reaching the optimal solution - Electricians time is binding - Technicians time is non-binding with Slack = 40. Constraint RHS: the value input for the RHS of each constraint equation 10

11 Sensitivity Report Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$5 Solution value CD players E+30 $C$5 Solution value Stereo receivers E Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $D$8 Electricians' Time $D$9 Audio Technicians' Time E Changes in RHS usually affect the size of the feasible region. - If the size of feasible region increases, optimal objective function improves - If the size of feasible region decreases, optimal objective function worsens Relationship expressed as Shadow Price. Impact of changes in RHS values is measured by the Shadow Price. 11

12 Sensitivity Report Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$5 Solution value CD players E+30 $C$5 Solution value Stereo receivers E Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $D$8 Electricians' Time $D$9 Audio Technicians' Time E Shadow Price is the change in optimal objective function value for one unit increase in RHS. Electrician s time is binding constraint; If Electrician s time increases, more products can be made, and profit will go up The amount of profit will change by for each additional unit of the binding resource is equal to the Shadow Price. For each additional hour of Electrician s time that firm can increase will increase the profit by $30. 12

13 Sensitivity Report Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$5 Solution value CD players E+30 $C$5 Solution value Stereo receivers E Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $D$8 Electricians' Time $D$9 Audio Technicians' Time E Allowable Increases & Allowable Decreases: Validity range for the shadow price. - For what level of increase of RHS value of the electricians time constraint is the shadow price of $30 valid? - The shadow price is valid only as long as the change in the RHS is within the Allowable Increase & Allowable Decrease values. 13

14 Sensitivity Report Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$5 Solution value CD players E+30 $C$5 Solution value Stereo receivers E Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $D$8 Electricians' Time $D$9 Audio Technicians' Time E Question: Assume we have an opportunity to get 50 additional hours of electricians time. However, this time will cost us an extra $20 per hour. Should we take it? Question: Can you solve the problem If we have 100 Electricians time If we have 60 Electricians time If we have 240 Electricians time If we have 0 Electricians time 14

15 Sensitivity Report Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$5 Solution value CD players E+30 $C$5 Solution value Stereo receivers E Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $D$8 Electricians' Time $D$9 Audio Technicians' Time E Technicians time has 40 unused hours. No interest in acquiring additional hours of resource. Shadow price for audio technicians time is zero. Allowable increase for RHS value is infinity. Once 40 hours is lost (current unused portion, or slack) of technicians time, resource also becomes binding. Any additional loss of time will clearly have adverse effect on profit. 15

16 Changes in a Right-Hand Side Receivers Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$5 Solution value CD players E+30 $C$5 Solution value Stereo receivers E Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $D$8 Electricians' Time $D$9 Audio Technicians' Time E Technician s time = 60 (3C+ S= 60) (2C+4S = 80) Electricians time increases from 80 to 100 (2C+4S = 100) CD players 16

17 Changes in a Right-Hand Side 60 Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease 50 $B$5 Solution value CD players E+30 $C$5 Solution value Stereo receivers E Receivers Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $D$8 Electricians' Time $D$9 Audio Technicians' Time E Electricians time decreases from 80 to CD players 17

18 Changes in a Right-Hand Side Receivers Summary in changes in RHS Changes in RHS usually affect the size of the feasible region. The location of the optimal corner point changes There is a range of values for each RHS in which the shadow price remains unchanged. 10 Electricians time = CD players 18

19 Manufacturing Application Anderson Electronics is considering producing four potential products: VCR Stereo TV DVD Supply Elct. Components ,700 Non-Elct. Components ,500 Assembly time ,500 Selling price $70 $80 $150 $110 Cost $41 $48 $78 $56 Profit $29 $32 $72 $54 Objective: Maximize profit 19

20 Questions Answer Report Anderson Electronics Answer Report Target Cell (Max) Cell Name Original Value Final Value $F$8 Profit $0.00 $69, Cell Name Original Value Final Value $B$5 Solution value VCR $C$5 Solution value Stereo $D$5 Solution value TV $E$5 Solution value DVD Cell Name Cell Value Formula Status Slack $F$10 Electronic comp $F$10<=$H$10 Binding 0.00 $F$11 Non-electronic comp $F$11<=$H$11 Not Binding $F$12 Assembly time $F$12<=$H$12 Binding 0.00 Question 1: What s the optimal production strategy? Question 2: What s maximum profit for A.E.? Question 3: Which resource is fully used up? Which constrain is exactly satisfied? 20

21 Questions Sensitivity Report Anderson Electronics Sensitivity Report Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$5 Solution value VCR E+30 $C$5 Solution value Stereo $D$5 Solution value TV E+30 $E$5 Solution value DVD Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $F$10 Electronic comp $F$11 Non-electronic comp E $F$12 Assembly time Question 1: What s the Shadow Price of electronic components? Question 2:What s the Allowable Range of RHS value of electronic components? Question 3: What s the impact on profit if we could increase the supply of non-electronic components by 400 units (to a total 4,900 units)? 21

22 Questions Sensitivity Report Anderson Electronics Sensitivity Report Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$5 Solution value VCR E+30 $C$5 Solution value Stereo $D$5 Solution value TV E+30 $E$5 Solution value DVD Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $F$10 Electronic comp $F$11 Non-electronic comp E $F$12 Assembly time Question 4: What s the impact on profit if we could increase the supply of electronic components by 400 units (to a total 5,100 units)? Question 5: What would happen if we could increase the supply of electronic components by 4000 units (to a total 8,700 units)? 22

23 Questions Sensitivity Report Question 6: For the question about getting an additional 400 units of electronic components, what would happen if the supplier of these 400 units wants $8 per unit (rather than the current cost of $7 per unit)? Question 7: Assume we have an opportunity to get 250 additional hours of assembly time. However, this time will cost us $15 per hour (rather than the current cost of $10 per hour). Should we take it? Question 8: If we force the production of VCR, what would be the impact on profit? Alternatively, how much profit must VCRs become before the firm should consider producing them? Question 9: Assume that there is uncertainty in the price of DVD. For what range of prices will the current production be optimal? Question 10: If DVD actually sold for less and profit per unit drops to $50, what would be the firm s new total profit? 23

24 Simultaneous Changes In Parameter Values Previous assumption: analyzing only one change at a time Possible to analyze impact of simultaneous changes on optimal solution only under specific condition 100% Rule: Σ (Change / Allowable change) 1 If sum does not exceed 1, information provided in sensitivity report is valid to analyze impact of changes. 24

25 Sensitivity Analysis Sensitivity analysis is used by management to answer a series of what if questions about inputs to LP model. Over what ranges can prices change without affecting the optimality of the present solution? Will the present solution remain the optimum solution if the amount of raw materials, production time, or storage space is suddenly changed? The amount of each type of resources needed to produce one unit of each type of product may vary slightly. Will such changes affect the optimal solution? 25

26 Sensitivity Analysis Sensitivity analysis is used to determine effects on the optimal solution within specified ranges for the objective function coefficients (OFCs), and right hand side (RHS) values. Basic Question: How does our solution change as the input parameters change? Allowable Range for OFCs Shadow prices Allowable Range for RHS values 26

MGSC 1205 Quantitative Methods I

MGSC 1205 Quantitative Methods I MGSC 1205 Quantitative Methods I Slides Five Multi-period application & Sensitivity Analysis Ammar Sarhan Multi-period Applications: Production Scheduling Most challenging application of LP is modeling

More information

Basic Linear Programming Concepts. Lecture 2 (3/29/2017)

Basic Linear Programming Concepts. Lecture 2 (3/29/2017) Basic Linear Programming Concepts Lecture 2 (3/29/2017) Definition Linear Programming (LP) is a mathematical method to allocate scarce resources to competing activities in an optimal manner when the problem

More information

Mid Term Solution. T7, T8, T20 pounds of tomatoes to sell in weeks 7, 8, 20. F7, F8, F20 - pounds of tomatoes to freeze in weeks 7, 8, 20.

Mid Term Solution. T7, T8, T20 pounds of tomatoes to sell in weeks 7, 8, 20. F7, F8, F20 - pounds of tomatoes to freeze in weeks 7, 8, 20. Leaders for Manufacturing 15.066J Summer 2003 S. C. Graves Mr. Smith s Garden FORMULATION Mid Term Solution Decision variables (5 points): there are decision variables for vegetables planted, for tomatoes

More information

A Production Problem

A Production Problem Session #2 Page 1 A Production Problem Weekly supply of raw materials: Large Bricks Small Bricks Products: Table Profit = $20/Table Chair Profit = $15/Chair Session #2 Page 2 Linear Programming Linear

More information

Digital Media Mix Optimization Model: A Case Study of a Digital Agency promoting its E-Training Services

Digital Media Mix Optimization Model: A Case Study of a Digital Agency promoting its E-Training Services Available online at: http://euroasiapub.org, pp. 127~137 Thomson Reuters Researcher ID: L-5236-2015 Digital Media Mix Optimization Model: A Case Study of a Digital Agency promoting its E-Training Services

More information

Econ 172A, Fall 2010: Quiz III IMPORTANT

Econ 172A, Fall 2010: Quiz III IMPORTANT Econ 172A, Fall 2010: Quiz III IMPORTANT 1. The quiz has 3 forms. You should answer the questions from only one form. If your student identification number ends in 1, 2, 3 answer the questions from Form

More information

CIS QA LEVEL 2 WEEK 5 TOPIC: LINEAR PROGRAMMING OBJECTIVE AND SHORT ANSWER QUESTIONS

CIS QA LEVEL 2 WEEK 5 TOPIC: LINEAR PROGRAMMING OBJECTIVE AND SHORT ANSWER QUESTIONS CIS QA LEVEL 2 WEEK 5 TOPIC: LINEAR PROGRAMMING OBJECTIVE AND SHORT ANSWER QUESTIONS 1. In the graphical method of solving a Linear Programming problem, the feasible region is the region containing A.

More information

Transshipment. Chapter 493. Introduction. Data Structure. Example Model

Transshipment. Chapter 493. Introduction. Data Structure. Example Model Chapter 493 Introduction The transshipment model is a special case of the minimum cost capacitated flow model in which there are no capacities or minimums on the arc flows. The transshipment model is similar

More information

Managerial Decision Modeling w/ Spreadsheets, 3e (Balakrishnan/Render/Stair) Chapter 2 Linear Programming Models: Graphical and Computer Methods

Managerial Decision Modeling w/ Spreadsheets, 3e (Balakrishnan/Render/Stair) Chapter 2 Linear Programming Models: Graphical and Computer Methods Managerial Decision Modeling w/ Spreadsheets, 3e (Balakrishnan/Render/Stair) Chapter 2 Linear Programming Models: Graphical and Computer Methods 2.1 Chapter Questions 1) Consider the following linear programming

More information

Chapter 11. Decision Making and Relevant Information Linear Programming as a Decision Facilitating Tool

Chapter 11. Decision Making and Relevant Information Linear Programming as a Decision Facilitating Tool Chapter 11 Decision Making and Relevant Information Linear Programming as a Decision Facilitating Tool 1 Introduction This chapter explores cost accounting for decision facilitating purposes It focuses

More information

S Due March PM 10 percent of Final

S Due March PM 10 percent of Final MGMT 2012- Introduction to Quantitative Methods- Graded Assignment One Grade S2-2014-15- Due March 22 11.55 PM 10 percent of Final Question 1 A CWD Investments, is a brokerage firm that specializes in

More information

Linear Programming. BUS 735: Business Decision Making and Research. Wednesday, November 8, Lecture / Discussion. Worksheet problem.

Linear Programming. BUS 735: Business Decision Making and Research. Wednesday, November 8, Lecture / Discussion. Worksheet problem. Linear Programming BUS 735: Business Decision Making and Research Wednesday, November 8, 2017 1 Goals and Agenda Learning Objective Learn how to formulate optimization problems with constraints (linear

More information

Linear Programming: Basic Concepts

Linear Programming: Basic Concepts Linear Programming: Basic Concepts Irwin/McGraw-Hill 1.١ The McGraw-Hill Companies, Inc., 2003 Introduction The management of any organization make Decision about how to allocate its resources to various

More information

QUANTITATIVE TECHNIQUES SECTION I

QUANTITATIVE TECHNIQUES SECTION I QUANTITATIVE TECHNIQUES SECTION I QUESTION ONE (a) In a recent research survey by Intelligence Consultants on the use of the services of auditing firms by various Non Governmental Organisations (NGOs)

More information

Chapter 1 Mathematical Programming: an overview

Chapter 1 Mathematical Programming: an overview Chapter 1 Mathematical Programming: an overview Companion slides of Applied Mathematical Programming by Bradley, Hax, and Magnanti (Addison-Wesley, 1977) prepared by José Fernando Oliveira Maria Antónia

More information

CHAPTER 5 SUPPLIER SELECTION BY LEXICOGRAPHIC METHOD USING INTEGER LINEAR PROGRAMMING

CHAPTER 5 SUPPLIER SELECTION BY LEXICOGRAPHIC METHOD USING INTEGER LINEAR PROGRAMMING 93 CHAPTER 5 SUPPLIER SELECTION BY LEXICOGRAPHIC METHOD USING INTEGER LINEAR PROGRAMMING 5.1 INTRODUCTION The SCMS model is solved using Lexicographic method by using LINGO software. Here the objectives

More information

THE UNIVERSITY OF BRITISH COLUMBIA Sauder School of Business SAMPLE MIDTERM EXAMINATION

THE UNIVERSITY OF BRITISH COLUMBIA Sauder School of Business SAMPLE MIDTERM EXAMINATION THE UNIVERSITY OF BRITISH COLUMBIA Sauder School of Business COMMERCE 290 INTRODUCTION TO QUANTITATIVE DECISION MAKING SAMPLE MIDTERM EXAMINATION PLEASE READ THE FOLLOWING: 1. This examination consists

More information

Transfer Pricing Cost Accounting Horngreen, Datar, Foster

Transfer Pricing Cost Accounting Horngreen, Datar, Foster Transfer Pricing Why Transfer Prices? Decentralized firms Decision-making power delegated to subunit-managers Intermediate products transferred from one subunit to another need to be priced Transfer prices

More information

DIS 300. Quantitative Analysis in Operations Management. Instructions for DIS 300-Transportation

DIS 300. Quantitative Analysis in Operations Management. Instructions for DIS 300-Transportation Instructions for -Transportation 1. Set up the column and row headings for the transportation table: Before we can use Excel Solver to find a solution to C&A s location decision problem, we need to set

More information

TRANSPORTATION PROBLEM AND VARIANTS

TRANSPORTATION PROBLEM AND VARIANTS TRANSPORTATION PROBLEM AND VARIANTS Introduction to Lecture T: Welcome to the next exercise. I hope you enjoyed the previous exercise. S: Sure I did. It is good to learn new concepts. I am beginning to

More information

Analysis of Electricity Markets. Lennart Söder

Analysis of Electricity Markets. Lennart Söder Analysis of Electricity Markets Lennart Söder Electric Power Systems Royal Institute of Technology March 2011 ii Contents 1 Basic electricity market modelling 1 1.1 Demand model...............................

More information

Homework 1 Fall 2000 ENM3 82.1

Homework 1 Fall 2000 ENM3 82.1 Homework 1 Fall 2000 ENM3 82.1 Jensen and Bard, Chap. 2. Problems: 11, 14, and 15. Use the Math Programming add-in and the LP/IP Solver for these problems. 11. Solve the chemical processing example in

More information

Analyzing Optimal Solutions Sensitivity Analysis

Analyzing Optimal Solutions Sensitivity Analysis time). If an increase or decrease falls within the range determined by the Allowable Increase and Allowable Decrease, then the Shadow Price will remain the same. For example, from the Sensitivity Report,

More information

MBF1413 Quantitative Methods

MBF1413 Quantitative Methods MBF1413 Quantitative Methods Prepared by Dr Khairul Anuar 1: Introduction to Quantitative Methods www.notes638.wordpress.com Assessment Two assignments Assignment 1 -individual 30% Assignment 2 -individual

More information

Linear Programming. 1 Goals and Agenda. Management 560: Management Science. Tuesday, March 17, 2009

Linear Programming. 1 Goals and Agenda. Management 560: Management Science. Tuesday, March 17, 2009 Linear Programming Management 560: Management Science Tuesday, March 17, 2009 1 Goals and Agenda Learning Objective Learn how to formulate optimization problems with constraints (linear programming problems).

More information

Transportation Problems

Transportation Problems C H A P T E R 11 Transportation Problems Learning Objectives: Understanding the feature of Assignment Problems. Formulate an Assignment problem. Hungarian Method Unbalanced Assignment Problems Profit Maximization

More information

Operation and supply chain management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology Madras

Operation and supply chain management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology Madras Operation and supply chain management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology Madras Lecture - 37 Transportation and Distribution Models In this lecture, we

More information

Linear Programming. Chapter 2: Basic Concepts. Lee-Anne Johennesse. Advanced Quantitative Methods 7 March 2016

Linear Programming. Chapter 2: Basic Concepts. Lee-Anne Johennesse. Advanced Quantitative Methods 7 March 2016 Linear Programming Chapter 2: Basic Concepts Lee-Anne Johennesse Advanced Quantitative Methods 7 March 2016 Linear Programming Chapter 2: Basic Concepts Introduction Part A The Wyndor Glass Company Product

More information

LINEAR PROGRAMMING APPROACHES TO AGGREGATE PLANNING. Linear programming is suitable to determine the best aggregate plan.

LINEAR PROGRAMMING APPROACHES TO AGGREGATE PLANNING. Linear programming is suitable to determine the best aggregate plan. LINEAR PROGRAMMING APPROACHES TO AGGREGATE PLANNING Linear programming is suitable to determine the best aggregate plan. Recall that linear programming assumes all variables are continuously divisible.

More information

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

MASSACHUSETTS INSTITUTE OF TECHNOLOGY MASSACHUSETTS INSTITUTE OF TECHNOLOGY 15.053 Optimization Methods in Management Science (Spring 2007) Recitation 4, March 1 st and March 2 nd, 2007 Problem 1: More Simplex Tableau Suppose while solving

More information

Short-Run Manufacturing Problems at DEC 2. In the fourth quarter of 1989, the corporate demand/supply group of Digital

Short-Run Manufacturing Problems at DEC 2. In the fourth quarter of 1989, the corporate demand/supply group of Digital Short-Run Manufacturing Problems at DEC 2 In the fourth quarter of 1989, the corporate demand/supply group of Digital Equipment Corporation (DEC) was under pressure to come up with a manufacturing plan

More information

P2 Performance Management

P2 Performance Management Performance Pillar P2 Performance Management Examiner s Answers SECTION A Answer to Question One (a) The standard cost of the actual hours worked was 3,493-85 = 3,408. At 12 per hour the actual hours worked

More information

Locational Marginal Pricing (LMP): Basics of Nodal Price Calculation

Locational Marginal Pricing (LMP): Basics of Nodal Price Calculation MRTU Locational Marginal Pricing (LMP): Basics of Nodal Price Calculation CRR Educational Class #2 CAISO Market Operations Why are LMPs important to the CRR Allocation & Settlement Process The CRR revenue

More information

Operations Research QM 350. Chapter 1 Introduction. Operations Research. University of Bahrain

Operations Research QM 350. Chapter 1 Introduction. Operations Research. University of Bahrain QM 350 Operations Research University of Bahrain INTRODUCTION TO MANAGEMENT SCIENCE, 12e Anderson, Sweeney, Williams, Martin Chapter 1 Introduction Introduction: Problem Solving and Decision Making Quantitative

More information

a. Show the feasible region. b. What are the extreme points of the feasible region? c. Find the optimal solution using the graphical procedure.

a. Show the feasible region. b. What are the extreme points of the feasible region? c. Find the optimal solution using the graphical procedure. Sheet 2-Chapter 2 PROBLEMS An Introduction to Linear Programming 11. Solve the following linear program using the graphical solution procedure: 12. Consider the following linear programming problem: a.

More information

Review Article Minimizing Costs Can Be Costly

Review Article Minimizing Costs Can Be Costly Advances in Decision Sciences Volume 2010, Article ID 707504, 16 pages doi:10.1155/2010/707504 Review Article Minimizing Costs Can Be Costly Rasmus Rasmussen Institute of Economics, Molde University College

More information

A Spreadsheet Approach to Teaching Shadow Price as Imputed Worth

A Spreadsheet Approach to Teaching Shadow Price as Imputed Worth A Spreadsheet Approach to Teaching Shadow Price as Imputed Worth Jerry D. Allison University of Central Oklahoma Edmond, OK 73034 Phone: (405) 974-5338 Fax: (405) 974-3821 Email: jallison@ucok.edu ABSTRACT

More information

Microeconomic Theory -1- Introduction and maximization

Microeconomic Theory -1- Introduction and maximization Microeconomic Theory -- Introduction and maximization Introduction Maximization. Profit maximizing firm with monopoly power 6. General results on maximizing with two variables 3. Non-negativity constraints

More information

1. Spatial Equilibrium Behavioral Hypotheses

1. Spatial Equilibrium Behavioral Hypotheses University of California, Davis Department of Agricultural and esource Economics AE 252 Optimization with Economic Applications Lecture Notes 12 Quirino Paris 1. patial Equilibrium Behavioral Hypotheses.......................................

More information

Using Excel s Solver

Using Excel s Solver Using Excel s Solver How to get the computer to do the work. A Profit Maximization Problem. Lecture 8 Slide 1 Is the Solver Installed If your Tools pulldown menu in Excel looks like this, without a Solver

More information

Modeling Linear Programming Problem Using Microsoft Excel Solver

Modeling Linear Programming Problem Using Microsoft Excel Solver Modeling Linear Programming Problem Using Microsoft Excel Solver ADEKUNLE Simon Ayo* & TAFAMEL Andrew Ehiabhi (Ph.D) Department of Business Administration, Faculty of Management Sciences, University of

More information

UNIVERSITY OF MORATUWA

UNIVERSITY OF MORATUWA UNIVERSITY OF MORATUWA MSC/POSTGRADUATE DIPLOMA IN FINANCIAL MATHEMATICS MA 5101 OPERATIONAL RESEARCH TECHNIQUE I THREE HOURS October 2008 Answer FIVE questions and NO MORE. Question 1 ALI Electronics

More information

UNIVERSITY OF ECONOMICS PRAGUE Faculty of Informatics and Statistics. Management Science. Jan Fábry

UNIVERSITY OF ECONOMICS PRAGUE Faculty of Informatics and Statistics. Management Science. Jan Fábry UNIVERSITY OF ECONOMICS PRAGUE Faculty of Informatics and Statistics Management Science Jan Fábry 2003 UNIVERSITY OF ECONOMICS PRAGUE Faculty of Informatics and Statistics Management Science Jan Fábry

More information

Applied Data Analysis (Operations Research)

Applied Data Analysis (Operations Research) Applied Data Analysis (Operations Research) Pongsa Pornchaiwiseskul Pongsa.P@chula.ac.th http://j.mp/pongsa Faculty of Economics Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics,

More information

1) Operating costs, such as fuel and labour. 2) Maintenance costs, such as overhaul of engines and spraying.

1) Operating costs, such as fuel and labour. 2) Maintenance costs, such as overhaul of engines and spraying. NUMBER ONE QUESTIONS Boni Wahome, a financial analyst at Green City Bus Company Ltd. is examining the behavior of the company s monthly transportation costs for budgeting purposes. The transportation costs

More information

Paper P2 Performance Management (Russian Diploma) Post Exam Guide May 2012 Exam. General Comments

Paper P2 Performance Management (Russian Diploma) Post Exam Guide May 2012 Exam. General Comments General Comments Overall, candidates performance was very good, with a significant increase in the pass rate compared to the previous exam sitting. The exam assessed a breadth of topics from across the

More information

Optimizing the supply chain configuration with supply disruptions

Optimizing the supply chain configuration with supply disruptions Lecture Notes in Management Science (2014) Vol. 6: 176 184 6 th International Conference on Applied Operational Research, Proceedings Tadbir Operational Research Group Ltd. All rights reserved. www.tadbir.ca

More information

Pricing Game under Imbalanced Power Structure

Pricing Game under Imbalanced Power Structure Pricing Game under Imbalanced Power Structure Maryam Khajeh Afzali, Poh Kim Leng, Jeff Obbard Abstract The issue of channel power in supply chain has recently received considerable attention in literature.

More information

Homework Assignment #2: Answer Sheet

Homework Assignment #2: Answer Sheet Econ 427 Energy Economics and Energy Security Professor Ickes Spring 2013 Homework Assignment #2: Answer Sheet 1. Consider an exhaustible resource problem with demand given by =100.Letthecost of extraction

More information

Application of Dynamic Programming Model to Production Planning, in an Animal Feedmills.

Application of Dynamic Programming Model to Production Planning, in an Animal Feedmills. Application of Dynamic Programming Model to Production Planning, in an Animal Feedmills. * Olanrele, Oladeji.O.,,2 Olaiya, Kamorudeen A. and 2 Adio, T.A.. The Polytechnic Ibadan, Mechatronics Engineering

More information

Goals and Agenda Linear Programming Shadow Prices. Linear Programming. BUS 735: Business Decision Making and Research. Wednesday, November 8, 2017

Goals and Agenda Linear Programming Shadow Prices. Linear Programming. BUS 735: Business Decision Making and Research. Wednesday, November 8, 2017 Wednesday, November 8, 2017 Goals Reading Goals of this class meeting 1/ 9 Specific Goals: Learn how to set up problems with Learn how to maximize or minimize objectives subject to Learn how to solve linear

More information

EXCEL PROFESSIONAL INSTITUTE. LECTURE 5 Holy

EXCEL PROFESSIONAL INSTITUTE. LECTURE 5 Holy EXCEL PROFESSIONAL INSTITUTE LECTURE 5 Holy Q1. a) Investment Appraisal Lecture 10 &11 i. Types of Investment and Capital Expenditure ii. Objectives of Investment appraisal iii. Investment Appraisal Techniques

More information

THE CATHOLIC UNIVERSITY OF EASTERN AFRICA A. M. E. C. E. A

THE CATHOLIC UNIVERSITY OF EASTERN AFRICA A. M. E. C. E. A THE CATHOLIC UNIVERSITY OF EASTERN AFRICA A. M. E. C. E. A MAIN EXAMINATION P.O. Box 6217 00200 Nairobi - KENYA Telephone: 891601-6 Fax: 24-20-8984 E-mail:academics@cuea.edu JANUARY APRIL 2014 TRIMESTER

More information

P2 Performance Management

P2 Performance Management Performance Pillar P2 Performance Management Examiner s Answers SECTION A Answer to Question One (a) (i) The optimum selling price occurs where marginal cost = marginal revenue. Marginal cost is assumed

More information

Introduction to Management Science, 11e (Taylor) Chapter 3 Linear Programming: Computer Solution and Sensitivity Analysis

Introduction to Management Science, 11e (Taylor) Chapter 3 Linear Programming: Computer Solution and Sensitivity Analysis Instant download and all chapters Test Bank Introduction to Management Science 11th Edition Bernard W. Taylor III https://testbankdata.com/download/test-bank-introduction-managementscience-11th-edition-bernard-w-taylor-iii/

More information

ECON 4550 (Summer 2014) Exam 3

ECON 4550 (Summer 2014) Exam 3 ECON 4550 (Summer 014) Exam 3 Name Multiple Choice Questions: (4 points each) 1. Bob owns a food truck. He offers senior citizens a 10% discount. This behavior by Bob is an example of A. First Degree Price

More information

9 The optimum of Oligopoly

9 The optimum of Oligopoly Microeconomics I - Lecture #9, December 1, 2008 9 The optimum of Oligopoly During previous lectures we have investigated two important forms of market structure: pure competition, where there are typically

More information

Department of Economics. Harvard University. Spring Honors General Exam. April 6, 2011

Department of Economics. Harvard University. Spring Honors General Exam. April 6, 2011 Department of Economics. Harvard University. Spring 2011 Honors General Exam April 6, 2011 The exam has three sections: microeconomics (Questions 1 3), macroeconomics (Questions 4 6), and econometrics

More information

OPERATIONS RESEARCH Code: MB0048. Section-A

OPERATIONS RESEARCH Code: MB0048. Section-A Time: 2 hours OPERATIONS RESEARCH Code: MB0048 Max.Marks:140 Section-A Answer the following 1. Which of the following is an example of a mathematical model? a. Iconic model b. Replacement model c. Analogue

More information

Commerce 295 Midterm Answers

Commerce 295 Midterm Answers Commerce 295 Midterm Answers October 27, 2010 PART I MULTIPLE CHOICE QUESTIONS Each question has one correct response. Please circle the letter in front of the correct response for each question. There

More information

Problem Set 4 Duality, Sensitivity, Dual Simplex, Complementary Slackness

Problem Set 4 Duality, Sensitivity, Dual Simplex, Complementary Slackness Problem Set 4 Duality, Sensitivity, Dual Simplex, Complementary Slackness AM121/ES121 Fall 2018 Due 5:00 PM, Tuesday, October 16, 2018 Announcements The assignment is due by 5:00 PM, Tuesday, October 16,

More information

Capacity Planning with Rational Markets and Demand Uncertainty. By: A. Kandiraju, P. Garcia-Herreros, E. Arslan, P. Misra, S. Mehta & I.E.

Capacity Planning with Rational Markets and Demand Uncertainty. By: A. Kandiraju, P. Garcia-Herreros, E. Arslan, P. Misra, S. Mehta & I.E. Capacity Planning with Rational Markets and Demand Uncertainty By: A. Kandiraju, P. Garcia-Herreros, E. Arslan, P. Misra, S. Mehta & I.E. Grossmann 1 Motivation Capacity planning : Anticipate demands and

More information

CHAPTER 5 SOCIAL WELFARE MAXIMIZATION FOR HYBRID MARKET

CHAPTER 5 SOCIAL WELFARE MAXIMIZATION FOR HYBRID MARKET 61 CHAPTER 5 SOCIAL WELFARE MAXIMIZATION FOR HYBRID MARKET 5.1 INTRODUCTION Electricity markets throughout the world continue to be opened to competitive forces. The underlying objective of introducing

More information

Ch.01 Introduction to Modeling. Management Science / Instructor: Bonghyun Ahn

Ch.01 Introduction to Modeling. Management Science / Instructor: Bonghyun Ahn Ch.01 Introduction to Modeling Management Science / Instructor: Bonghyun Ahn Chapter Topics The Management Science Approach to Problem Solving Model Building: Break-Even Analysis Computer Solution Management

More information

OPERATIONAL CASE STUDY February 2018 EXAM ANSWERS. Variant 2. The February 2018 exam can be viewed at

OPERATIONAL CASE STUDY February 2018 EXAM ANSWERS. Variant 2. The February 2018 exam can be viewed at OPERATIONAL CASE STUDY February 2018 EXAM ANSWERS Variant 2 The February 2018 exam can be viewed at SECTION 1 - BRIEFING NOTE CORPORATE AND SOCIAL RESPONSIBILITY (CSR) REPORTING What we should include

More information

Operations Research Models and Methods Paul A. Jensen and Jonathan F. Bard. Inventory Level. Figure 4. The inventory pattern eliminating uncertainty.

Operations Research Models and Methods Paul A. Jensen and Jonathan F. Bard. Inventory Level. Figure 4. The inventory pattern eliminating uncertainty. Operations Research Models and Methods Paul A. Jensen and Jonathan F. Bard Inventory Theory.S2 The Deterministic Model An abstraction to the chaotic behavior of Fig. 2 is to assume that items are withdrawn

More information

Business Mathematics / Quantitative Research Methods I

Business Mathematics / Quantitative Research Methods I Faculty of Economics and Business Administration Exam: Code: Examinator: Co-reader: Business Mathematics / Quantitative Research Methods I E_BK1_BUSM / E_IBA1_BUSM / E_EBE1_QRM1 dr. R. Heijungs dr. G.J.

More information

Inventory Management 101 Basic Principles SmartOps Corporation. All rights reserved Copyright 2005 TeknOkret Services. All Rights Reserved.

Inventory Management 101 Basic Principles SmartOps Corporation. All rights reserved Copyright 2005 TeknOkret Services. All Rights Reserved. Inventory Management 101 Basic Principles 1 Agenda Basic Concepts Simple Inventory Models Batch Size 2 Supply Chain Building Blocks SKU: Stocking keeping unit Stocking Point: Inventory storage Item A Loc

More information

COB291, Management Science, Test 3, Fall 2008 DO NOT TURN TO THE NEXT PAGE UNTIL YOU ARE INSTRUCTED TO DO SO!

COB291, Management Science, Test 3, Fall 2008 DO NOT TURN TO THE NEXT PAGE UNTIL YOU ARE INSTRUCTED TO DO SO! COB291, Management Science, Test 3, Fall 2008 Name DO NOT TURN TO THE NEXT PAGE UNTIL YOU ARE INSTRUCTED TO DO SO! The following exam consists of FIVE problems for a total of 200 points. Please keep three

More information

INSTRUCTIONS. Supply Chain Management and LEAN concept simulation

INSTRUCTIONS. Supply Chain Management and LEAN concept simulation Supply Chain Management and LEAN concept simulation INSTRUCTIONS Welcome to ChainSim training manual. ChainSim is an online-based educational simulation in which the student will manage the supply chain

More information

ECON 8010 (Spring 2013) Exam 3

ECON 8010 (Spring 2013) Exam 3 ECON 8010 (Spring 2013) Exam 3 Name Multiple Choice Questions: (4 points each) 1. Nash s Existence Theorem states that A. an equilibrium exists in any game of incomplete information, but never exists in

More information

7,5 ECTS. Industrial Business Economics II IBE2. The exam is given to: Name: (Filled by student) Personal number: (Filled by student)

7,5 ECTS. Industrial Business Economics II IBE2. The exam is given to: Name: (Filled by student) Personal number: (Filled by student) Industrial Business Economics II 7,5 ECTS Ladokcode: The exam is given to: 41T10B IBE2 Name: (Filled by student) Personal number: (Filled by student) Date of exam: Thursday, 31 of May, 2012 Time: 09.00

More information

Performance Management

Performance Management Monitoring Test MT Performance Management F5PM-MTA-Z6-A Answers & Marking Scheme 06 DeVry/Becker Educational Development Corp. RODBER CO Linear programming model x = monthly production of product X y =

More information

Linear Programming 1 WENDY DESCRIBES THE CASE

Linear Programming 1 WENDY DESCRIBES THE CASE KEATMX03_p001-029.qxd 11/4/05 4:15 PM Page 1 Linear Programming 1 WENDY DESCRIBES THE CASE The Maximus Computer Company (MCC) has four basic computers it sells to students and small businesses. The first,

More information

Excel Solver Tutorial: Wilmington Wood Products (Originally developed by Barry Wray)

Excel Solver Tutorial: Wilmington Wood Products (Originally developed by Barry Wray) Gebauer/Matthews: MIS 213 Hands-on Tutorials and Cases, Spring 2015 111 Excel Solver Tutorial: Wilmington Wood Products (Originally developed by Barry Wray) Purpose: Using Excel Solver as a Decision Support

More information

AN ECONOMIC ANALYSIS OF THE EMISSION REDUCTION MARKET SYSTEM IN CHICAGO. Chao-Ning Liao and Hayri Onal * Long Beach, California, July 28-31, 2002

AN ECONOMIC ANALYSIS OF THE EMISSION REDUCTION MARKET SYSTEM IN CHICAGO. Chao-Ning Liao and Hayri Onal * Long Beach, California, July 28-31, 2002 AN ECONOMIC ANALYSIS OF THE EMISSION REDUCTION MARKET SYSTEM IN CHICAGO by Chao-Ning Liao and Hayri Onal * Selected Paper, American Agricultural Economics Association Meeting, Long Beach, California, July

More information

This is a refereed journal and all articles are professionally screened and reviewed

This is a refereed journal and all articles are professionally screened and reviewed Advances in Environmental Biology, 6(4): 1400-1411, 2012 ISSN 1995-0756 1400 This is a refereed journal and all articles are professionally screened and reviewed ORIGINAL ARTICLE Joint Production and Economic

More information

Programmed to pass. calculate the shadow price of direct labour

Programmed to pass. calculate the shadow price of direct labour Programmed to pass Ian Janes, CIMA course leader at Newport Business School, supplies and explains the answers to the supplementary question asked in March 2011 Financial Management s graphical linear

More information

Decision making and Relevant Information

Decision making and Relevant Information Decision making and Relevant Information 1 Introduction This chapter explores the decision-making process. It focuses on specific decisions such as accepting or rejecting a one-time-only special order,

More information

Techniques of Operations Research

Techniques of Operations Research Techniques of Operations Research C HAPTER 2 2.1 INTRODUCTION The term, Operations Research was first coined in 1940 by McClosky and Trefthen in a small town called Bowdsey of the United Kingdom. This

More information

DEVELOPMENT OF A DYNAMIC PROGRAMMING MODEL FOR OPTIMIZING PRODUCTION PLANNING. the Polytechnic Ibadan, Mechatronics Engineering Department; 3, 4

DEVELOPMENT OF A DYNAMIC PROGRAMMING MODEL FOR OPTIMIZING PRODUCTION PLANNING. the Polytechnic Ibadan, Mechatronics Engineering Department; 3, 4 DEVELOPMENT OF A DYNAMIC PROGRAMMING MODEL FOR OPTIMIZING PRODUCTION PLANNING 1 Olanrele, O.O., 2 Olaiya, K. A., 3 Aderonmu, M.A., 4 Adegbayo, O.O., 5 Sanusi, B.Y. 1, 2,5 the Polytechnic Ibadan, Mechatronics

More information

COMM 290 MIDTERM/FINAL EXAM REVIEW SESSION BY TONY CHEN

COMM 290 MIDTERM/FINAL EXAM REVIEW SESSION BY TONY CHEN COMM 290 MIDTERM/FINAL EXAM REVIEW SESSION BY TONY CHEN TABLE OF CONTENTS I. Vocabulary Overview II. Solving Algebraically and Graphically III. Understanding Graphs IV. Fruit Juice Excel V. More on Sensitivity

More information

Technical Bulletin Comparison of Lossy versus Lossless Shift Factors in the ISO Market Optimizations

Technical Bulletin Comparison of Lossy versus Lossless Shift Factors in the ISO Market Optimizations Technical Bulletin 2009-06-03 Comparison of Lossy versus Lossless Shift Factors in the ISO Market Optimizations June 15, 2009 Comparison of Lossy versus Lossless Shift Factors in the ISO Market Optimizations

More information

Chapters 1 and 2 Trade Without Money and A Model of Money

Chapters 1 and 2 Trade Without Money and A Model of Money Chapters 1 and 2 Trade Without Money and A Model of Money Main Aims: 1. Answer following two questions: Why money is used as a medium of exchange? How and why money improves allocations in an economy and

More information

PRODUCTION MANAGEMENT ANALYSIS USING MONTE CARLO METHOD

PRODUCTION MANAGEMENT ANALYSIS USING MONTE CARLO METHOD PRODUCTION MANAGEMENT ANALYSIS USING MONTE CARLO METHOD Renata Walczak Warsaw University of Technology, College of Economics and Social Sciences Lukasiewicza 17, 09-400 Plock, Poland Abstract The article

More information

Effect of Transportation Model on Organizational Performance: A Case Study of MTN Nigeria, Asaba, Delta State, Nigeria

Effect of Transportation Model on Organizational Performance: A Case Study of MTN Nigeria, Asaba, Delta State, Nigeria International Journal of Innovative Social Sciences & Humanities Research 6(2):76-82, April-June, 2018 SEAHI PUBLICATIONS, 2018 www.seahipaj.org ISSN: 2354-2926 Effect of Transportation Model on Organizational

More information

Modelling Financial Flow of the Supply Chain

Modelling Financial Flow of the Supply Chain Modelling Financial Flow of the Supply Chain M.H Jahangiri 1, F.Cecelja 2 1 Department of Chemical and Process Engineering, University of Surrey, UK 2 Department of Chemical and Process Engineering, University

More information

The Transportation and Assignment Problems. Hillier &Lieberman Chapter 8

The Transportation and Assignment Problems. Hillier &Lieberman Chapter 8 The Transportation and Assignment Problems Hillier &Lieberman Chapter 8 The Transportation and Assignment Problems Two important special types of linear programming problems The transportation problem

More information

Model Question Paper with Solution

Model Question Paper with Solution Annexure P Model Question Paper with Solution Section A (Very Short Answer Questions) Q.1. Write down three differences between PERT and CPM in brief? Ans.1. The Program Evaluation and Review Technique

More information

LECTURE 2 SINGLE VARIABLE OPTIMIZATION

LECTURE 2 SINGLE VARIABLE OPTIMIZATION LECTURE 2 SINGLE VARIABLE OPTIMIZATION QUESTIONS/ISSUES TO ADDRESSED: 1. How did calculus made its way into Economics? 2. Why is the optimization hypothesis widely used? 3. How should one view optimization-based

More information

OPTIMIZATION OF ROCK STONE SELECTION IN SHORE PROTECTION PROJECTS - CASE STUDY: GAZA BEACH CAMP SHORE PROTECTION PROJECT

OPTIMIZATION OF ROCK STONE SELECTION IN SHORE PROTECTION PROJECTS - CASE STUDY: GAZA BEACH CAMP SHORE PROTECTION PROJECT OPTIMIZATION OF ROCK STONE SELECTION IN SHORE PROTECTION PROJECTS - CASE STUDY: GAZA BEACH CAMP SHORE PROTECTION PROJECT ABSTRACT Rifat N. Rustom 1 and Omar Al-Tabbaa 2 Rock stone of different sizes are

More information

MAN256 Introduction to Management Science

MAN256 Introduction to Management Science MAN256 Introduction to Management Science Sections 01 & 02 FINAL EXAM May 21, 2004, 15:00 Student Name: Student Number: Notes: The exam s duration is 135 minutes. Use your time efficiently. This is a closed-book

More information

Code No: RR Set No. 1

Code No: RR Set No. 1 Code No: RR410301 Set No. 1 IV B.Tech I Semester Regular Examinations, November 2007 OPERATIONS RESEARCH ( Common to Mechanical Engineering, Mechatronics and Production Engineering) Time: 3 hours Max Marks:

More information

Modeling Using Linear Programming

Modeling Using Linear Programming Chapter Outline Developing Linear Optimization Models Decision Variables Objective Function Constraints Softwater Optimization Model OM Applications of Linear Optimization OM Spotlight: Land Management

More information

Check HW: WS Calculator Linear Programming

Check HW: WS Calculator Linear Programming Check HW: WS Calculator Linear Programming A calculator company produces a scientific calculator and a graphing calculator. Long-term projections indicate an expected demand of at least 100 scientific

More information

The Ascending Bid Auction Experiment:

The Ascending Bid Auction Experiment: The Ascending Bid Auction Experiment: This is an experiment in the economics of decision making. The instructions are simple, and if you follow them carefully and make good decisions, you may earn a considerable

More information

David Simchi-Levi M.I.T. November 2000

David Simchi-Levi M.I.T. November 2000 Dynamic Pricing to improve Supply Chain Performance David Simchi-Levi M.I.T. November 2000 Presentation Outline The Direct-to-Consumer Model Motivation Opportunities suggested by DTC Flexible Pricing Strategies

More information

You can find the consultant s raw data here:

You can find the consultant s raw data here: Problem Set 1 Econ 475 Spring 2014 Arik Levinson, Georgetown University 1 [Travel Cost] A US city with a vibrant tourist industry has an industrial accident (a spill ) The mayor wants to sue the company

More information

CHAPTER THREE DEMAND AND SUPPLY

CHAPTER THREE DEMAND AND SUPPLY CHAPTER THREE DEMAND AND SUPPLY This chapter presents a brief review of demand and supply analysis. The materials covered in this chapter provide the essential background for most of the managerial economic

More information

Modeling of competition in revenue management Petr Fiala 1

Modeling of competition in revenue management Petr Fiala 1 Modeling of competition in revenue management Petr Fiala 1 Abstract. Revenue management (RM) is the art and science of predicting consumer behavior and optimizing price and product availability to maximize

More information